An additional pragmatic benefit to this approach is that it affords us access to a roster of techniques designed for covariant classical field theories, but which can be used for an ED that is indeterministic and quantum. Indeed, once a Hamiltonian framework is adopted, we can borrow the techniques of Dirac [1]}[2]} in his development of parameterized field theories. That is, for the task of depicting the changing surface geometry we treat the surface variables \(X^{\mu }_{x}\)  as if they were dynamical variables too. This is accomplished by formally introducing the auxiliary variables \(\pi _{\mu }(x)=\pi _{\mu x}\)  that will play the role of momenta conjugate to \(X_{x}^{\mu }\) . These \(\pi \) 's are defined through the Poisson bracket (PB) relations,
\(\left\lbrace  X_{x}^{\mu },X_{x^{\prime }}^{\nu }\right\rbrace =0\,,\quad \left\lbrace  \pi _{\mu x},\pi _{\nu x^{\prime }}\right\rbrace =0\,,\quad \left\lbrace  X_{x}^{\mu },\pi _{\nu x^{\prime }}\right\rbrace =\delta _{\nu }^{\mu }\delta (x,x^{\prime })~. \) 
